Ultra-low noise cryogenic microwave amplification

ABSTRACT

Embodiments of the microwave amplification system are described. In an embodiment, a microwave amplification system includes a microwave amplifier that contains a paramagnetic material with an impurity. The impurity has a plurality of nuclear spin and electron spin-based energy levels. The system includes an input to receive a pumping signal which is transmitted to the microwave amplifier to cause a population inversion in the impurity and excite it to one of the nuclear spin and electron spin-based energy levels. The system further includes another input to receive an input signal to be amplified by the microwave amplifier, the input signal having a lower power than the pumping signal. Once transmitted to the microwave amplifier, the input signal is amplified by the excited state of the impurity in the microwave amplifier thereby generating an amplified signal.

BENEFIT CLAIM

This application claims the benefit under 35 U.S.C. § 119(e) ofprovisional application 62/813,537, filed Mar. 4, 2019, the entirecontents of which is hereby incorporated by reference for all purposesas if fully set forth herein.

FIELD OF THE TECHNOLOGY

The present invention relates to the field of electronic signalamplification, in particular to ultra-low noise cryogenic microwaveamplification.

BACKGROUND

The approaches described in this section are approaches that could bepursued, but not necessarily approaches that have been previouslyconceived or pursued. Therefore, unless otherwise indicated, it shouldnot be assumed that any of the approaches described in this sectionqualify as prior art merely by virtue of their inclusion in thissection.

Quantum-level signals at microwave frequencies require ultra-lowtemperature operations. For example, the required temperature may varyfrom 10 to 100 millikelvin, because the energy of thermal noise k_(B)Tof the environment has to be much lower than the energy of a singlequanta ℏω at a microwave frequency (microwave photon), where k_(B) isBoltzmann's constant (=1.38×10⁻²³ J/K=1.38×10⁻²³ m²kgs⁻²K⁻¹), ℏ thereduced Planck's constant (1.05×10⁻³⁴ m² kg s⁻¹). Accordingly, for the 5GHz microwave, the corresponding temperature is,

$\frac{\hslash\omega}{k_{B}} \approx {250{{mK}.}}$Because of the low energy of microwave signals at the quantum level,amplification of microwave signals, especially low-noise amplification,at millikelvin environments is extremely challenging. However, suchamplification is very important, if not necessary, for quantum computingtechnology and its applications.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings of certain embodiments in which like reference numeralsrefer to corresponding parts throughout the figures:

FIG. 1A is a block diagram that depicts an example quantum microwaveamplification system for a “quantum DUT” (device-under-test) in atransmission measurement, and FIG. 1B is a block diagram that depicts anexample quantum microwave amplification system for reflectionmeasurement, in one or more embodiments;

FIG. 2 is a block diagram that depicts a microwave amplification systemwith a Josephson parametric amplifier (JPA) at millikelvin temperaturesfor quantum-based signal, with further amplification at 3-4K, and atroom temperature, in an embodiment;

FIG. 3A, FIG. 3B and FIG. 3C are diagrams that describe an example of amaser operation, in one or more embodiments;

FIG. 4A and FIG. 4B are diagrams that depict an example operation ofthree-level maser with a pump signal, in one or more embodiments;

FIG. 5A is a diagram that depicts a crystallographic schematic of a “P1center,” a nitrogen impurity in a diamond, in an embodiment;

FIG. 5B is an energy level diagram that depicts the energy levels ofeach state versus constant magnetic field B₀ that is parallel to thecrystallographic [001] axis, in an embodiment;

FIG. 6A and FIG. 6B are diagrams that depict a process of inversionthrough cross-relaxation of a diamond maser for transition frequenciesat a fixed magnetic field of a P1 center for each nuclear spin, in oneor more embodiments;

FIG. 7 is a block diagram that depicts quantum system 700 for microwaveamplification, in an embodiment;

FIG. 8 is a photo that depicts a microwave resonator, in an embodiment;

FIG. 9 is a diagram that depicts an example gain of microwave quantumamplification system 700, in an embodiment;

FIG. 10 is a block diagram that depicts quantum system 1000 formicrowave amplification, in an embodiment;

FIG. 11 is a diagram that depicts the gain spectrum of resulting signalof microwave quantum amplification system 1000, in an embodiment;

FIG. 12 is a flow diagram that depicts a process of microwaveamplification in a paramagnetic material with an impurity, in anembodiment;

FIG. 13 is a block diagram that depicts an example of a maser amplifierapplication to microwave quantum information and technology, in anembodiment;

FIG. 14 is a diagram that depicts a traveling-wave maser amplifier, inan embodiment.

DETAILED DESCRIPTION

In the following description, for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the various embodiments. It will be apparent, however,that embodiments may be practiced without these specific details. Inother instances, structures and devices are depicted in block diagramform in order to avoid unnecessarily obscuring the embodiments.

General Overview

Quantum technology-based techniques for amplifying microwave signals atmillikelvin environments are described. The signals may includequantum-based information (qubit) carrying signal, magnetic resonance,or any other signal at microwave frequencies. Using the approachesdescribed herein microwave signals are amplified with a higher dynamicrange than the prior art and without any other noise besides the lownoise due to a quantum mechanical fluctuation.

The amplification of microwave signal is generated based on impurityspins in a solid crystal, which is placed in a microwave resonator orembedded in a waveguide. The approaches maintain the advantages ofJosephson parametric amplifiers (JPA) for quantum technology andapplications but with a much higher dynamic range. In addition, theproposed amplification techniques functions under magnetic field, whichJPA also lacks. Any quantum device, which works at microwave frequenciesin a refrigerator and operates with superconducting or semiconductingquantum bits, quantum dots, mechanical resonators, or spins, may usethese techniques.

Quantum Signal Noise Overview

In an embodiment, the signal-to-noise ratio of a system, and thus itsperformance, is determined by the noise added by the first amplifier.Such noise may be characterized by the noise power spectral density S(ω)at the signal frequency ω. As a figure-of-merit for amplifiers, thisnoise level is often expressed in the dimension of temperature

${T_{N}\left\lbrack {= \frac{s(\omega)}{k_{B}}} \right\rbrack},$referred to as a noise temperature. Accordingly, the noise may depend onthe temperature of the environment.

The number of noise photons added by the amplifier having a noisetemperature T_(N) is expressed by

$n = {\left( {e^{\frac{\hslash\omega}{k_{B}T_{N}}} - 1} \right)^{- 1}.}$For example, one of the low-noise cryogenic microwave amplifiers is ahigh electron mobility transistor (HEMT) amplifier, whose typical noisetemperature is about 3-5 K, i.e., adding more than 10 noise photons. Thelower limit of T_(N) is given by zero-point energy fluctuation ℏω/2because of the quantum mechanical uncertainty.

Therefore, in order to maximize the signal-to-noise ratio of themicrowave measurement for a quantum DUT, the first amplifier should havea noise temperature as close as possible to the zero-point energyfluctuation, i.e.,

${T_{N0} = \frac{\hslash\omega}{2k_{B}}}.$

FIG. 1A and FIG. 1B are block diagrams that depict a system with aJosephson parametric amplifier (JPA) operating at millikelvintemperature, in one or more embodiments. Josephson parametric amplifiers(JPA) 120 is based on superconducting circuits in which Josephsonjunctions (superconducting tunnel junctions) are embedded. Suchamplifiers exploit the nonlinearity of Josephson junctions, and areoperated at temperatures much lower than the energy of the microwavesignals, i.e.,

${T \ll \frac{\hslash\omega}{k_{B}}},$in the millikelvin temperature range. JPAs have better performance asthe amplifier typically add n=0.5 to 1 noise photons. The systems100(a)/(b) may further include microwave resonator 110 which containssample(s) at millikelvin, inside a dilution refrigerator.

FIG. 1A is a block diagram that depicts an example quantum system fortransmission measurement, in an embodiment, and FIG. 1B is a blockdiagram that depicts an example quantum system for reflectionmeasurement, in an embodiment. Probe microwave signal 151 is sent toquantum DUT 110, and either transmitted signal 153 a in system 100(a) orreflected signal 153 b in system 100(b) is routed to JPA 120, whichamplifies the signal (signal 155). As depicted in FIG. 1B, JPA 120 mayfunction in reflection too. In either case, amplified signal 155 isstill small compared with the room temperature thermal noise. Therefore,it is further amplified at higher temperature stages, in an embodiment(see also FIG. 2 ).

FIG. 2 is a block diagram that depicts a system with a Josephsonparametric amplifier (JPA) at millikelvin temperatures for quantum-basedsignal, with further amplification at 3-4K, and at room temperature, inan embodiment. In such an embodiment, JPA generated signal 155 of system100(a)/(b), as an example, is further amplified typically once at 3-4 K(210) by cryogenic HEMT amplifier 215 of system 200, and once again atroom temperature by amplifier 220 to generate amplified signal 250.Signal 250 is detected by receiver circuit 230, typically in eitherhomodyne or heterodyne detection, as an example.

Although system 200 may amplify the quantum-based signals, system 200suffers from a limited dynamic range. This is due to JPA 120 (and JPAsin general) having limited dynamic range, i.e., due to having very lowinput saturation power. For example, JPA 120 may have a maximum inputpower of about −100 dBm (0.1 picowatts). Using such JPA 120 would limitsystem 200 to reading simultaneously only theoretically twentyquantum-bits (qubits), and however, in practice, further reduced to fivequantum-bits.

Another approach for amplifying microwave signals is a maser (“microwaveamplification by stimulated emission of radiation”), with spins insolids. FIG. 3A, FIG. 3B and FIG. 3C are diagrams that describe anexample of a maser operation, in one or more embodiments. In FIG. 3A, amaser operation is depicted that includes a quantum mechanical energylevel system in its equilibrium, in an embodiment. The lower energylevel and upper energy level are the ground, |g

(310 a), and the excited, |e

(320 b), states, respectively, which are separated by the energy of ℏω.Here, ℏω»k_(B)T is assumed.

In FIG. 3B, the diagram depicts a population inversion, where the upperlevel 320 b is more populated than the lower level 310 b. When apopulation of a quantum mechanical energy level is caused to be inverted(in FIG. 3B), the amplification occurs due to stimulated emission (asdepicted in FIG. 3C). Accordingly, FIG. 3C depicts an amplification ofsignal 350 by stimulated emission of radiation 355, in an embodiment.

The challenge of the maser-based approach is how to excite the quantummechanical system into a situation, in which the population is inverted.To address this challenge, techniques described herein utilize a systemwhich has multiple energy levels, at least having three levels.

FIG. 4A and FIG. 4B are diagrams that depict an example operation of athree-level maser with a pump signal, in an embodiment. In such anembodiment, the inversion is achieved by utilizing another level |f

(430 a and 430 b). In FIG. 4A, strong pump signal 450 with energy of ℏω′excites the population from the ground state |g

, 410 a, to the third level (|f

), 430 a/b, which is above the first excited state |e

, 420 a/b, in the energy level. Subsequently, the population goes, fromthe state |f

, 430 b, to the second level |e

, 420 b, resulting in a creation of population inversion at state 420 b,which are separated from ground state |g

, 410 b, by an energy of ℏω.

In such an embodiment, it is assumed that the probability of thetransition between |e

, 420 b, and |f

, 430 b, states are high. Thus, the population |f>-state, 430 a is goingto immediately relax into |e

, 420 b. As a result of the relaxation, the population for thetransition between |g

, 410 b, and |e

, 420 b, states will be able to be inverted by “pumping” the transitionbetween |g

, 410 a, to |f

, 430 a states. This three-level maser scheme may be realized inparamagnetic materials, which possess multiple energy levels, such asruby (chromium-doped sapphire).

The noise performance of the maser amplifier may reach the quantummechanical lower limit

$T_{N0} = \frac{\hslash\omega}{2k_{B}}$provided that it is operated at extremely low temperature, such that

${T \ll \frac{\hslash\omega}{k_{B}}},$and the spin relaxation rate is lower than the pumping rate.

The former is nowadays always the case in the quantum information andtechnology applications at microwave frequencies in a dilutionrefrigerator. The latter is also the case at millikelvin temperatures,where the spin-lattice relaxation path, which is the dominant relaxationmechanism at a higher temperature, is frozen out, resulting in extremelyslow relaxation (typically˜min, sometimes even˜hour).

Impurity Crystal-Based Maser Overview

In an embodiment, a maser system is operated using a crystal withimpurities. FIG. 5A is a diagram that depicts a crystallographicschematic of “P1 center in diamond”, a nitrogen impurity in a diamond,in an embodiment. P1 center is an example of one of the stable impuritycenters in diamond.

In an embodiment, due to placing diamond crystals at millikelvintemperature, the impurity generates spins that are fully polarized inthe quantum ground state. The relaxation process for such a paramagneticmaterial is a spin-lattice relaxation, which may add significant noisefor the maser amplification at high temperatures. However, therelaxation process at millikelvin temperatures are extremely long,sometimes reaching hours. Therefore, it produces negligible noise.

In an embodiment, the quantum system uses a pumping microwave frequency,which has a lower frequency than the signal frequency rather than usinga higher frequency than that of the signal. Despite using a lowerpumping frequency than the signal frequency, the system continues toproduce a population inversion.

One technique to achieve inversion with lower pumping frequency thanthat of the signal is to use P1 centers in diamond (FIG. 5A). Althoughthe approaches herein describe using P1 centers for impurity and diamondas a paramagnetic material, the techniques described herein are notlimited to P1 centers and/or diamonds. Other impurities and paramagneticmaterials may be used in the techniques described herein to achievesimilar results.

In an embodiment, an impurity structure introduces multiple energylevels for stimulated emission. The energy levels may be based on thepermutation pairs of the electron spin and nuclear spin of a P1 center.If an impurity possesses possible three nuclear spins and two electronspins, then a total of six different energy levels are introduced to thesystem for stimulating emission.

FIG. 5B is an energy level diagram that depicts the energy level of eachstate versus constant magnetic field B₀ that is parallel to thecrystallographic [001] axis, in an embodiment. The energy levels aregenerated due to hyperfine interaction between the electron spin and thenuclear spin. In such an embodiment, the P1 center of FIG. 5A possessesan electron spin of one half (m_(s)=±½) and nuclear spin of one(m_(I)=−1, 0, +1), which split the electron spin resonance transition(−½↔+½) into three, each of which corresponds to one of the nuclear spinstates, as depicted in FIG. 5B. Thus, in total, there are six energylevels. In FIG. 5(b) the three states corresponding to (m_(S)=+½) arelabeled as 512, 514, 516, and the other three states corresponding tom_(S)=−½ are labeled 522, 524, 526. In the right hand panel of FIG. 5B,a zoom of 502 and 504 of the left hand panel of FIG. 5B is depicted.

In the P1 center example, the frequencies of the three transitions(between 526 and 516, 524 and 514, and 522 and 512, respectively) areequally spaced, as depicted by the distance between lines 516 and 514,between lines 512 and 514, between lines 522 and 524, and between lines524 and 526 in FIG. 5B. Thus, the energy required to flip two spins inthe central transition (of m_(I)=0, between 524 and 514) is the same asthe one to flip each one spin in the transitions on both sides (between526 and 516, and between 522 and 512) simultaneously. This process isreferred to herein as “cross-relaxation,” an example of which isdepicted in FIG. 6A.

FIG. 6A and FIG. 6B are diagrams that depict a process of inversionthrough cross-relaxation of a diamond maser under a fixed magneticfield, in an embodiment. The population inversion may be realized bypumping the central transition (between 524 and 514 of FIG. 5B.) Themicrowave pump transfers the population from the state 524 to the state514. The cross-relaxation process leads to population from the state 514returning back to 524 and at the same time the populations from thestates 526 and 522 transferring to the upper states 516 and 512,respectively. In addition, the population from each of the three upperstates, 512, 514, 516 relaxes to the corresponding lower state 522, 524,526 due to the spin-lattice relaxation.

In an embodiment, an asymmetry of the relaxation rate exists between thetwo transitions on each side (between 526 and 516, and between 522 and512 of FIG. 6 ) is assumed to exist. Moreover, the time required for thecross-relaxation is assumed to be shorter than the time for thespin-lattice relaxation of each transition. And, experimentally, it hasbeen verified that both are indeed satisfied.

In such a situation, population inversion would be established in eitherthe upper level 512 or 516. For example, if the relaxation rate of thetransition on the right-hand side (from 512 to 526) is much greater thanthat of the left hand side (from 516 to 526), the population in the lefttransition will keep pumped in the upper state 516, as depicted in FIG.6B.

The above-described relaxation conditions occur for P1 centers indiamond in the presence of another type of defect centers, such as anitrogen-vacancy (NV) center. NV centers have electronic spin 1. In astatic magnetic field above 100 mT, the resonant frequencies of the NVcenters are close to that of P1 centers. For techniques using thediamond crystal, NV centers are distributed over the same volume in adensity of about 2 ppm. P1 centers and NV centers may exchange energyvia spin flip-flop transitions and other higher-order cross-relaxationprocesses. The interaction between the spins of P1 and N-V centers leadsto an accelerated relaxation of the P1 centers in the state 512 and tothe enhanced population of the state 516, and eventually to thepopulation inversion at the transition between the states 526 and 516.

System Overview

FIG. 7 is a block diagram that depicts microwave quantum amplificationsystem 700 for microwave amplification, in an embodiment. Microwavequantum amplification system 700 includes dilution refrigerator 702 witha base temperature of about 10 mK. Diamond crystal 720 is placed inloop-gap microwave resonator 718 (an example of which is depicted inFIG. 8 ) within copper enclosure 716. Loop-gap microwave resonator 718is thermally anchored to the 10 mK plate of dilution refrigerator 702,in an embodiment. Constant magnetic field B₀ is generated by asuperconducting coil and applied to diamond 720 along itscrystallographic axis.

In an embodiment, the transmission spectra are measured by transmittingprobing microwave input signal 752 to resonator 718 through coaxialcables with a series of attenuations 710 and 712. Attenuators 710 and712 suppress thermal noise coming from room temperature through themicrowave coaxial cables at temperature stages of 3 or 4 K and 100 mK,respectively.

In an embodiment, the microwave signals originate from microwaveresonator 718 pass through (series of) cryogenic isolators 722 and a lowpass filter 724, which filters out the high band noise and any remnantsof pump signal 750. The signal may then be further amplified by highelectron mobility transistor (HEMT) cryogenic amplifier 726 at 3-4 K andmay be further followed by another amplifier, amplifier 730, at the roomtemperature. Cryogenic isolators 722 serve to prevent noise signalsgenerated by the HEMT amplifier from entering back into resonator 718,in an embodiment.

To perform the maser-based amplification, B₀ magnetic field is tuned tosuch magnitude that the central spin transition (“m_(I)=0”, between 524and 514 of FIG. 5B and also see FIG. 6A and FIG. 6B) is matched to thefrequency of microwave resonator 718, in an embodiment. An examplemagnetic field B₀ of about 189 millitesla is applied for the results inFIG. 9 , but this value of magnetic field B₀ may change depending on theoperating frequency of resonator 718. Pumping signal 750 strongly drivesthe central spin transition of P1 centers (between 524 and 514), forexample, with a power of a few microwatts at the resonator frequency toresonator 718 to cause population inversion of the impurity as describedfor FIG. 5A, FIG. 5B, FIG. 6A and FIG. 6B.

In an embodiment, to determine the maser amplifier's gain, the magneticfield, B₀, is changed to about 186 milli-Tesla, where the low fieldtransition (m_(I)=+1, between 516 and 526 of FIG. 5B) frequency ismatched to the frequency, ω_(r), of resonator 718. (Changing theconstant magnetic field B₀ is not necessary though, as described furtherbelow.) Amplified signal 754 is measured at room temperature, assimilarly described for FIGS. 2 and 7 , by sending a weak probemicrowave signal (˜femtowatt) as input signal 752. FIG. 9 is a diagramthat depicts an example gain of quantum system 700, in an embodiment.The gain is measured to be more than 30 dB, as depicted in FIG. 9 , andthe example bandwidth as narrow as ˜100 kHz.

FIG. 10 is a block diagram that depicts quantum system 1000 formicrowave amplification, as an alternative embodiment. Unlike quantumsystem 700 that uses microwave transmission, microwave reflectioncoefficient is measured in system 1000 (see also FIG. 1B, system 100(b))by putting circulator 1002 and isolator 1004 before microwave resonator718 so that the outgoing signals, such as signal 1056, are routed tocold HEMT amplifier 726 and the following measurement chain. Althoughthe alternative embodiment describes the reflection-based measurement,the embodiment may be modified for the transmission measurement.

In system 1000, cancellation line 1070 is also installed to suppress anyunwanted effects by the strong pump signal 1050, which may distort themeasurement. To this end, the microwave signal for the pump 1050 issplit into two by directional coupler 1006; one is used for pump line1072, and the other is for cancellation line 1070. The split pumpsignals are separately sent to the inside of the dilution refrigeratorthrough each temperature stage 706, 704, and 702. The cancellationsignal is combined by directional coupler 1008 back with the reflectedpump signal out of resonator 718's after circulator 1002 and isolator1010 at 10 mK in refrigerator 702. The phase and amplitude of thecancellation signal are tuned to have 180 degrees shifted and the sameamplitude as of the reflected pump signal 1050 by phase shifter 1012 andvariable attenuator 1014, respectively, so that the strong pump signal1050 reflected from the resonator 718 coming into directional coupler1008 is canceled out.

In an embodiment, B₀ is fixed such that the high-energy spin transition(m_(I)=+1, between 516 and 526) matches the frequency of microwaveresonator 718 (ω_(r)=6.385 GHz in this example). The spins are pumped bysending strong microwave signal 1050 with a power of a few microwatts,as an example, at the frequency of ω_(p)=6.293 GHz, which isoff-resonant with resonator 718 but resonant with the central spintransition (m_(I)=0, between 514 and 524), in this example.

System 1000 may be probed by sending weak microwave signal 1052 (˜<−100dBm) across ω_(r) and measuring the reflected signal at the samefrequency. Resulting signal 1054 of system 1000 is analyzed by a vectornetwork analyzer (VNA).

FIG. 11 is a diagram that depicts the gain spectrum of resulting signal1052 of system 1000, in an embodiment. In such an embodiment, themaximum gain was measured to be about 37 dB with a bandwidth of about100 kHz. The gain profile may be tunable over a wide frequency range byadjusting the value of the resonator frequency ω_(r) of 718 and thestatic magnetic field B₀.

Functional Overview

FIG. 12 is a flow diagram that depicts a process of quantum microwaveamplification in a paramagnetic material with an impurity, in anembodiment. At step 1205, a magnetic field is applied to theparamagnetic material along the crystallographic axis. The applicationof a magnetic field generates, at step 1210, multiple possible energylevels for the population corresponding to nuclear and electron spins.Each combination of nuclear and electron spins corresponds to a uniqueenergy level. In an embodiment, possible energy levels for a particularelectron spin are equally spaced.

At step 1215, receiving a pump signal and transmitting the pump signal,at step 1220, to the paramagnetic material with the impurity. Thepumping signal provides the additional energy that transfer thepopulation to an initial excited state that corresponds to a differentelectron spin state than the initial ground state of the impurity. Atstep 1225, due to the cross-relaxation described in FIG. 6B, or due tospin-lattice relaxations, the paramagnetic spin system is transferred tothe excited states, which may correspond to a different nuclear spinstate or a different electron spin state. The energy level of the newexcited state is determined by the static magnetic field B₀ applied andthe strength of the pumping signal (power/frequency, see FIG. 5A andFIG. 5B), in an embodiment.

At step 1230, an input microwave signal to amplify arrives at thesystem. The signal is then routed through the paramagnetic material ofthe maser amplifier, at step 1235, and is, thereby, amplified by themaser amplifier, at step 1240, as described in FIG. 3A, FIG. 3B, FIG.3C, FIG. 4A and FIG. 4B embodiments. The resulting signal may betransmitted as an output of the maser amplifier, at step 1245, and/orfurther amplified by non-cryogenic environment amplifiers such as HEMTat 4K (or similar temperatures) and additional amplifiers at roomtemperatures.

In an embodiment, one or more low pass filters and attenuators may beused to reduce the thermal noise. Alternatively or additionally, acancellation signal may be generated, at step 1250, by phase-shifting(180 degrees) and tuning the amplitude by variable attenuators to thesame as of the pump signal coming out of the maser amplifier. Thecancelation signal is used to cancel out the remnants of the pump signalin the amplified input signal, at step 1255. The resulting outputsignal, at step 1245, has less noise.

Quantum System Noise Performance

The noise temperature of the invented maser amplifier is characterizedusing alternative techniques. Using the first technique, magnetic fieldB₀ is fixed such that the central P1 center spin transition (m_(I)=0,between 514 and 524 see FIG. 5B, FIG. 6A and FIG. 6B) matches to thefrequency of microwave resonator 718, which is about 189 milli-Tesla,for example (although this value may change in each experiment dependingon the resonator frequency). The central P1 center spin transition maybe pumped by sending a strong microwave signal with a power of a fewmicrowatt at the resonator frequency (ω_(r)=5.384 GHz), as an example.Magnetic field B₀ is then changed to about 186 millitesla (likewise,this value may also change in each experiment depending on the resonatorfrequency), where the low field transition (m_(I)=+1) frequency matchedto the resonator frequency ω_(r). A spectrum analyzer may be used tomeasure the noise power spectral density of the system (see also nextparagraph).

Using a different technique of noise temperature characterization, B₀ isfixed such that the high-energy spin transition (m_(I)=+1, 516 and 526)matches the frequency of the microwave resonator, and the central spintransition (m_(I)=0, 514 and 524) is pumped by sending a strongmicrowave signal with a power of a few micro-Watts, as an example.Instead of sending a probe microwave signal into the resonator, thenoise power spectrum at the resonator frequency is measured using aspectrum analyzer, in an embodiment. The resulting total noisetemperature T_(N)+T_(bath) is estimated to be about 0.6 K. This suggeststhat the maser amplifier described herein has a noise temperature ofabout 0.4 K, which is very close to

${T_{N0} \approx \frac{\hslash\omega}{2k_{B}}} = {{0.1}5K}$(for 6 GHz microwave), assuming that the thermal photon noise T_(bath)inside the resonator is as low as the vacuum noise, which is equal toT_(N0). The obtained noise temperature, which is slightly higher thanthe quantum limited, may attribute to the insufficient attenuation andfiltering of systems 700 and 1000, which may have increased the thermalphoton noise T_(bath) to 0.3 K or more, resulting in increasing thetotal noise temperature.

The dynamic range of the maser amplifier may be evaluated. The powerdependence of the gain is measured by changing the probe microwavesignal power, in an embodiment. The saturation power is estimated atleast to be about 0.1 nanowatts, which is more than three orders ofmagnitude higher than that of the value of 0.1 picowatts of thestate-of-the-art JPAs. It was confirmed that this saturation isattributed to the saturation of the cryogenic HEMT amplifier. Thisimplies that the actual saturation power of the maser amplifier inventedis much higher.

Quantum Information Input-Based System Overview

FIG. 13 is a block diagram that depicts an example of a maser amplifierapplication to microwave quantum information science and technology, inan embodiment. In FIG. 13 , the microwave signal coming out of quantumDUT 1310, which contains quantum information of 1310, such as a state ofqubit(s) (referenced as signal 1356), is sent to maser amplifier 1320through circulator 1302. Accordingly, signal 1356 gets amplified throughmaser amplifier 1320. This amplified signal is further amplified by aHEMT amplifier at a higher temperature stage, if necessary, followed byanother amplifier at room temperature (examples of which are depicted inFIGS. 2, 7, and 10 ) and is measured by a receiver circuit, in the sameway as in FIG. 2 .

Pump microwave signal 1350 may be separately fed to maser amplifier 1320through another dedicated microwave line, passing through coupler orcombiner, such as 1308. This strong pump signal may be canceled usingsimilar techniques as discussed above in FIG. 8 . Alternatively oradditionally, the remnants of strong pump signal 1350 may be dissipatedat a higher temperature stage. For example, the remnant of strong pumpsignal 1350 may be routed to another microwave line by a microwavediplexer, which is placed between the coldest temperature stage (10-100mK) and HEMT at 3-4 K.

The bandwidth of a microwave amplifier may be described in terms ofgain-bandwidth product

${G^{\frac{1}{2}} \cdot B},$where G is the power gain, and B is the bandwidth of the amplifier. Forexample, the example maser amplifier demonstrated in this invention mayhave a gain-bandwidth of about 5-15 MHz. Example JPAs (Josephsonparametric amplifier) have a gain-bandwidth range from 10 MHz to morethan 10 GHz.

Travelling-Wave Amplifier

In an embodiment, a maser amplifier comprises of a chain of maseramplifiers to improve the gain-bandwidth. Instead of putting aparamagnetic crystal in a microwave resonator, as depicted in FIG. 7 , atransmission line (waveguide) is patterned directly on top of theparamagnetic crystal. The transmission line may be of various types,e.g., stripline or coplanar waveguide. Such an arrangement yields a“traveling-wave” maser amplifier. FIG. 14 is a schematic that depicts atraveling-wave maser amplifier, in an embodiment.

The traveling-wave maser may include a transmission line on top of aruby crystal. Such devices may have a gain-bandwidth product of about500 MHz or more.

In an embodiment, the microwave transmission line is a losslesssuperconducting material, such as Nb, NbTi, TiN, or NbTiN, whichsuppresses ohmic losses inside the amplifier, resulting in a furtherimprovement of the gain. Moreover, operating, such a traveling-wavemaser amplifier, at a millikelvin temperature enhances the polarizationof spins in the lowest energy level by more than one order of magnitude.Such an environment increases the effective number of spins whichcontributes to the amplification process (as depicted in FIG. 3A, FIG.3B, FIG. 3C, FIG. 4A and FIG. 4B), resulting in even further improvementof the gain.

In an embodiment, the magnetic field gradient may be applied to theparamagnetic maser crystal to further increase the bandwidth of atraveling-guide maser amplifier. Such a gradient makes the electron spinresonance transition frequencies inhomogeneous over the crystal, i.e.,increase the linewidth of the transition, therefore increasing thebandwidth of the maser amplifier can be enhanced, which is beneficial tothe applications to quantum technology, such as the example describedfor FIG. 13 .

What is claimed is:
 1. A microwave amplification system comprising: amicrowave amplifier comprising a paramagnetic material that includes animpurity, the impurity having a plurality of nuclear spin and electronspin-based energy levels for the impurity; an input to receive a pumpingsignal; an input to receive an input signal to be amplified by themicrowave amplifier, wherein the input signal has lower power than thepumping signal; wherein the pumping signal causes, at a millikelvintemperature range, a population inversion to an excited state to atleast one energy of the plurality of nuclear spin and electronspin-based energy levels of at least one excited nuclear spin state;wherein the population inversion causes amplification of the inputsignal, thereby generating an amplified signal.
 2. The system of claim1, wherein the paramagnetic material comprising the impurity, is placedin a microwave resonator that is coupled to a dilution refrigerator. 3.The system of claim 1, wherein the microwave amplifier is a masermicrowave amplifier.
 4. The system of claim 1, wherein the paramagneticmaterial is a diamond crystal, and the impurity is a nitrogen impuritywithin the diamond crystal.
 5. The system of claim 1, wherein a magneticfield is applied to the paramagnetic material, thereby generatingexcited states for impurity population of the impurity.
 6. The system ofclaim 1, wherein each unique excited state corresponds to a uniquecombination of a nuclear spin and electron spin of the impurity.
 7. Thesystem of claim 1, wherein energy levels, of the plurality of energylevels, that correspond to a same electron spin but a different nuclearspin, are equally spaced.
 8. The system of claim 1, wherein the pumpsignal causes an initial population inversion to an initial excitedstate of an initial ground state of the impurity, wherein the initialexcited state is different from the initial ground state by at least thedifference in an electron spin of the impurity.
 9. The system of claim1, wherein the population inversion is caused by cross-relaxation of aninitial excited state into the excited state, wherein the excited stateis different from the initial excited state by at least the differencein a nuclear spin of the impurity.
 10. The system of claim 1, whereinthe amplification of the input signal is performed through release ofenergy from a relaxation of the population inversion from the excitedstate to a ground state of the excited state.
 11. The system of claim 1,wherein the pump signal has a lower frequency than the input signal. 12.The system of claim 1, further comprising: a phase shifter, the phaseshifter receiving the pump signal and generating a phase-shifted signal,cancellation signal, of the pump signal; a directional coupler to mergethe cancellation signal with the amplified signal to cancel at least aportion of the pump signal for the amplified signal.
 13. The system ofclaim 1, wherein the microwave amplifier comprises a transmission linecoupled to the input to receive the input signal, the transmission linerouting the input signal through a plurality of impurities of theparamagnetic material that includes the impurity.
 14. A methodcomprising: receiving, at a first input of a microwave amplifier, apumping signal; receiving, at a second input of the microwave amplifier,an input signal to be amplified, wherein the input signal has lowerpower than the pumping signal; transmitting the pumping signal to aparamagnetic material of the microwave amplifier to cause, at amillikelvin temperature range, a population inversion to an excitedstate in the paramagnetic material corresponding to at least one energylevel; wherein the at least one energy level is generated by theexistence of an impurity in the paramagnetic material, the impurityhaving one or more spin states of: a nuclear spin states and one or moreelectron spin states; wherein unique combinations of each of the one ormore nuclear spin and the one or more electron spin states correspond toa plurality of energy levels that include the at least one energy levelat the millikelvin temperature range; transmitting the input signalthrough the paramagnetic material of the microwave amplifier in theexcited state; based, at least in part, on transmitting the input signalthrough the paramagnetic material in the excited state, amplifying theinput signal based on the at least one energy level, thereby generatingan amplified signal.
 15. The method of claim 14, further comprisingapplying a magnetic field to the paramagnetic material, therebygenerating the plurality of energy levels.
 16. The method of claim 14,further comprising: the pump signal transforming an initial ground stateof the impurity to an initial excited state, wherein the initial excitedstate is different from the initial ground state by at least thedifference in an electron spin of the impurity.
 17. The method of claim14, further comprising: generating the population inversion bycross-relaxation of an initial excited state into the excited state,wherein the excited state is different from the initial excited state byat least the difference in a nuclear spin of the impurity.
 18. Themethod of claim 14, further comprising amplifying the input signalthrough a release of energy from a relaxation of the populationinversion from the excited state to a ground state of the excited state.19. The method of claim 14, wherein the pump signal has a lowerfrequency than the input signal.
 20. The method of claim 14, furthercomprising: phase-shifting the pump signal thereby generating aphase-shifted signal, cancellation signal, of the pump signal; mergingthe cancellation signal with the amplified signal to cancel at least aportion of the pump signal for the amplified signal.
 21. The system ofclaim 1, wherein the millikelvin temperature range is from 10millikelvin to 100 millikelvin.
 22. The method of claim 14, wherein themillikelvin temperature range is from 10 millikelvin to 100 millikelvin.